. Please show work on how 2theta is calculated into sine 2 theta. Step by step based on the info given.

Worked Example Consider the following XRD pattern for Aluminum, which was collected using CuKa radiation. Intensity (%) (38.43,100.0) 100 90 80 + ALUMINIUM a =1.540562 70 60 50 + (44.67,46.9) 40 30 (65.02,26.4) (78.13,27.9) (116.36,11.9) 20 (82.33,7.8) 10 (111.83,12.2)V (98.93,3.6) D 2002 0 0 5 10 15 20 25 30 3540 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 Index this pattern and determine the lattice parameters. Steps: (1) Identify the peaks. (2) Determine sine. (3) Calculate the ratio sin O/(integers) (4) Identify the lowest common quotient from (3) and identify the integers to which it corresponds. Let the lowest common quotient be K. (5) Divide sin? 0 by K for each peak. This will give you a list of integers corresponding to h + k +1?. (6) Select the appropriate pattern of h? +k+1? values and identify the Bravais lattice. (7) Calculate lattice parameters. Here we go again! (1) Identify the peaks. sin sin'e Peak No. sin e 2 sin 3 sin e 4 sin e 5 sin e 6 8 001 AWN 1 2 3 4 5. 6 7 8 20 38.43 44.67 65.02 78.13 82.331 98.931 111.83 116.36 0